Merit aid for USAMO-level math students?

My 9th-grade son is a top math student (even by CC standards, I think) and probably a pretty average CC student otherwise. His stats:

  • qualified to take the USAJMO this year
  • way too many lower math awards
  • 36 math ACT (33 composite) as a freshman
  • will take Discrete Math this summer, BC calculus next year, MV Calculus/Linear Algebra/AP Stats as a junior, and probably Diff Eq/upper-level prob and stats as a senior.

Our “problem,” so to speak, is that we make too much money for need aid and too little money to pay $300k for each of our kids to go to school. So the MITs/CalTechs/Ivys of the world are out. We’re looking for some good schools, with strong math/CS programs (he’s looking to double-major in both), that he might have a chance to get merit scholarship from to get the COA down to…$100k? $130k? Maybe 150k?

Our son knows how much we’re willing to spend, by the way, so he doesn’t have heart set on any particular college. He thinks of it like a math problem to be solved, so he wants to apply to 15-20 schools to try to find the optimal merit/cost combination. (Maybe I can talk him out of quite that many.)

Anyway, any ideas for colleges that might fit his need would be appreciated. We’re from the Midwest, but he’s willing to go anywhere.

Carnegie Mellon U.